1. Splash Screen

2. Five-Minute Check (over Lesson 4–2) CCSS Then/Now New Vocabulary
Key Concept: Point-Slope Form
Example 1: Write and Graph an Equation in Point-Slope Form
Concept Summary: Writing Equations
Example 2: Writing an Equation in Standard Form
Example 3: Writing an Equation in Slope-Intercept Form
Example 4: Point-Slope Form and Standard Form
Lesson Menu

3. Write an equation of the line that passes through the given point and has the given slope. (5, –7), m = 3
A. y = 22x + 3
B. y = 22x – 3
C. y = 3x + 22
D. y = 3x – 22
5-Minute Check 1

4. Write an equation of the line that passes through the given point and has the given slope. (5, –7), m = 3
A. y = 22x + 3
B. y = 22x – 3
C. y = 3x + 22
D. y = 3x – 22
5-Minute Check 1

5. Write an equation of the line that passes through the given point and has the given slope. (1, 5),B. C. D.
5-Minute Check 2

6. Write an equation of the line that passes through the given point and has the given slope. (1, 5),B. C. D.
5-Minute Check 2

7. Which equation is the line that passes through the points (6, –3) and (12, –3)?
A. y = –3x + 1
B. y = –3x
C. y = –3
D. y = 3x
5-Minute Check 3

8. Which equation is the line that passes through the points (6, –3) and (12, –3)?
A. y = –3x + 1
B. y = –3x
C. y = –3
D. y = 3x
5-Minute Check 3

9. Which equation is the line that passes through the points (9, –4) and (3, –6)?
A. y = –3x – 7 B. C.
D. y = x + 7
5-Minute Check 4

10. Which equation is the line that passes through the points (9, –4) and (3, –6)?
A. y = –3x – 7 B. C.
D. y = x + 7
5-Minute Check 4

11. Identify the equation for the line that has an x-intercept of –2 and a y-intercept of 4.
A. y = –2x + 4
B. y = 2x + 4
C. y = 2x – 4
D. y = 4x – 2
5-Minute Check 5

12. Identify the equation for the line that has an x-intercept of –2 and a y-intercept of 4.
A. y = –2x + 4
B. y = 2x + 4
C. y = 2x – 4
D. y = 4x – 2
5-Minute Check 5

13. Which is an equation of the graph shown?B.
C. y = –2x + 3
D. y = 2x + 3
5-Minute Check 5

14. Which is an equation of the graph shown?B.
C. y = –2x + 3
D. y = 2x + 3
5-Minute Check 5

15. Mathematical Practices 2 Reason abstractly and quantitatively.
Content Standards
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Mathematical Practices
2 Reason abstractly and quantitatively.
Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
CCSS

16. Write equations of lines in point-slope form.
You wrote linear equations given either one point and the slope or two points.
Write equations of lines in point-slope form.
Write linear equations in different forms.
Then/Now

17. point-slope form
Vocabulary

18. Concept 1

19. Write and Graph an Equation in Point-Slope Form
Write the point-slope form of an equation for a line that passes through (–2, 0) with slope
Point-slope form
(x1, y1) = (–2, 0)
Simplify.
Answer:
Example 1

20. Write and Graph an Equation in Point-Slope Form
Write the point-slope form of an equation for a line that passes through (–2, 0) with slope
Point-slope form
(x1, y1) = (–2, 0)
Simplify.
Answer:
Example 1

21. Graph the equation Plot the point at (–2, 0).
Write and Graph an Equation in Point-Slope Form
Graph the equation
Plot the point at (–2, 0).
Use the slope to find another point on the line. Draw a line through the two points.
Answer:
Example 1

22. Graph the equation Plot the point at (–2, 0).
Write and Graph an Equation in Point-Slope Form
Graph the equation
Plot the point at (–2, 0).
Use the slope to find another point on the line. Draw a line through the two points.
Answer:
Example 1

23. Write the point-slope form of an equation for a line that passes through (4, –3) with a slope of –2.
A. y – 4 = –2(x + 3)
B. y + 3 = –2(x – 4)
C. y – 3 = –2(x – 4)
D. y + 4 = –2(x – 3)
Example 1

24. Write the point-slope form of an equation for a line that passes through (4, –3) with a slope of –2.
A. y – 4 = –2(x + 3)
B. y + 3 = –2(x – 4)
C. y – 3 = –2(x – 4)
D. y + 4 = –2(x – 3)
Example 1

25. Concept 2

26. Multiply each side by 4 to eliminate the fraction.
Writing an Equation in Standard Form
In standard form, the variables are on the left side of the equation. A, B, and C are all integers.
Original equation
Multiply each side by 4 to eliminate the fraction.
Distributive Property
Example 2

27. Subtract 3x from each side.
Writing an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
Subtract 3x from each side.
–3x + 4y = –20
Simplify.
3x – 4y = 20
Multiply each side by –1.
Answer:
Example 2

28. Subtract 3x from each side.
Writing an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
Subtract 3x from each side.
–3x + 4y = –20
Simplify.
3x – 4y = 20
Multiply each side by –1.
Answer: The standard form of the equation is 3x – 4y = 20.
Example 2

29. Write y – 3 = 2(x + 4) in standard form.
A. –2x + y = 5
B. –2x + y = 11
C. 2x – y = –11
D. 2x + y = 11
Example 2

30. Write y – 3 = 2(x + 4) in standard form.
A. –2x + y = 5
B. –2x + y = 11
C. 2x – y = –11
D. 2x + y = 11
Example 2

31. Distributive Property
Writing an Equation in Slope-Intercept Form
Original equation
Distributive Property
Add 5 to each side.
Example 3

32. Simplify. Answer: Writing an Equation in Slope-Intercept Form
Example 3

33. Answer: The slope-intercept form of the equation is
Writing an Equation in Slope-Intercept Form
Simplify.
Answer: The slope-intercept form of the equation is
Example 3

34. Write 3x + 2y = 6 in slope-intercept form.A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Example 3

35. Write 3x + 2y = 6 in slope-intercept form.A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Example 3

36. A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD.
Point-Slope Form and Standard Form
A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD.
Write an equation in point-slope form for the line containing the side BC.
___
Example 4

37. Step 1 Find the slope of BC.
Point-Slope Form and Standard Form
Step 1 Find the slope of BC.
Slope formula
(x1, y1) = (4, 3) and
(x2, y2) = (6, –2)
Example 4

38. Step 2 You can use either point for (x1, y1) in the point-slope form.
Point-Slope Form and Standard Form
Step 2 You can use either point for (x1, y1) in the point-slope form.
Using (4, 3)
Using (6, –2)
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Example 4

39. Step 2 You can use either point for (x1, y1) in the point-slope form.
Point-Slope Form and Standard Form
Step 2 You can use either point for (x1, y1) in the point-slope form.
Using (4, 3)
Using (6, –2)
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Example 4

40. B. Write an equation in standard form for the same line.
Point-Slope Form and Standard Form
B. Write an equation in standard form for the same line.
Original equation
Distributive Property
Add 3 to each side.
2y = –5x + 26
Multiply each side by 2.
5x + 2y = 26
Add 5x to each side.
Answer:
Example 4

41. B. Write an equation in standard form for the same line.
Point-Slope Form and Standard Form
B. Write an equation in standard form for the same line.
Original equation
Distributive Property
Add 3 to each side.
2y = –5x + 26
Multiply each side by 2.
5x + 2y = 26
Add 5x to each side.
Answer: 5x + 2y = 26
Example 4

42. A. The figure shows right triangle ABC
A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x + 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
Example 4

43. A. The figure shows right triangle ABC
A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x + 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
Example 4

44. B. The figure shows right triangle ABC
B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2
Example 4

45. B. The figure shows right triangle ABC
B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2
Example 4

46. End of the Lesson